Find the variance and standard deviation of 62,65, 57, 62, 56,

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486. Find the variance and standard deviation of 62,65, 57, 62, 56, 51, 69, 60.


                         x = 62, 65, 57, 62, 56, 51, 69, 60
rightwards double arrow                  sum straight x space equals space 482 comma space straight N space equals space 8
rightwards double arrow                   top enclose straight x space equals space fraction numerator sum straight x over denominator straight N end fraction equals 482 over 8 equals 60.25
which is not a whole number.
As values of x are large, we shall use formula
                straight sigma squared space equals space fraction numerator straight N sum straight d squared minus left parenthesis sum straight d right parenthesis squared over denominator straight N squared end fraction
Let                          A = 60
                               d = x - A = x - 60 = 2, 5, -3, 2, -4, -9, 9, 0
rightwards double arrow                         sum straight d equals 2
Now,                        straight d squared equals left parenthesis 2 right parenthesis squared comma space left parenthesis 5 right parenthesis squared comma space left parenthesis negative 3 right parenthesis squared comma space left parenthesis 2 right parenthesis squared comma space left parenthesis negative 4 right parenthesis squared comma space left parenthesis negative 9 right parenthesis squared space left parenthesis 9 right parenthesis squared comma space left parenthesis 0 right parenthesis squared
rightwards double arrow                       sum straight d squared equals 4 plus 25 plus 9 plus 4 plus 16 plus 81 plus 81 plus 0 equals 220
∴                      straight sigma squared space equals space fraction numerator straight N sum straight d squared minus left parenthesis sum straight d right parenthesis squared over denominator straight N squared end fraction equals fraction numerator 8 left parenthesis 220 right parenthesis minus left parenthesis 2 right parenthesis squared over denominator left parenthesis 8 right parenthesis squared end fraction equals fraction numerator 1760 minus 4 over denominator 64 end fraction equals 1756 over 64 equals 27.4
∴   Variance left parenthesis straight sigma squared right parenthesis space equals space 27.4
                 S.D. left parenthesis straight sigma right parenthesis space equals space square root of 27.4 end root space equals space 5.23

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